| Abstract: The subject of my talk is a joint work
with Sergey Fomin (the preprint is available at http://front.math.ucdavis.edu/hep-th/0111053).
We study Y-systems, a particular class of birational recurrence relations
associated with an arbitrary finite root system. These relations were introduced
by Al.B.Zamolodchikov, they arise in the theory of thermodynamic Bethe
ansatz. Rather unexpectedly, the machinery developed in our study of Y-systems
allows us to introduce a new family of simplicial complexes associated
to root systems. In type A, our construction produces Stasheff's associahedron,
whereas in type B it gives the Bott-Taubes polytope, or cyclohedron. |
